SOLUTION: Show,without solving an equation that the roots of 2xsquared +(2k-1)x=K are Rational for all rational values of K

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Question 1112295: Show,without solving an equation that the roots of 2xsquared +(2k-1)x=K are Rational for all rational values of K
Answer by ikleyn(52865) About Me  (Show Source):
You can put this solution on YOUR website!
.
The given equation 

2x^2 +(2k-1)x = k  



is equivalent to

2x^2 +(2k-1)x - k = 0



which, in turn, is factored as


(2x-1)*(x+k) = 0


and, OBVIOUSLY, has the roots  x= 1%2F2  and  x= k,  that are rational numbers.

Solved and Proved.